Q.A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle to the nearest minute, through which it will turn in 30 seconds.

Step 1: Speed $=36$ km/hr $=\frac{36\times1000}{3600}=10$ m/s.

Step 2: Distance in $30$ s $=10\times30=300$ m $=0.3$ km.

Step 3: $\theta = \frac{s}{r} = \frac{0.3}{1} = 0.3$ radian. …

Convert the speed to consistent units, find the distance travelled in 30 s, use θ = s/r (radian), then conv …

• Forgetting to convert the speed from km/hr to m/s (or the radius from km to m) before dividing, causing a units mismatch.
• Using 60 seconds instead of 30 seconds for the time interval. …